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# Find all elliptic curves of conductor Andrei Jorza, Jen Balakrishnan, and I verified that the Stein-Watkins tables
   http://modular.math.washington.edu/Tables/ecdb/

are complete for prime conductors . This proved that the smallest conductor of a rank elliptic curve is not prime. Is the smallest conductor ? To find out, one has to compute every elliptic curve (up to isogeny) of conductor . Cremona has computed every curve of conductor , and much more about each curve (e.g., pretty much everything we know how to compute about a curve).

Problem 4.2.1   Determine all elliptic curves over of conductor . By determine'' this could be man finding just the first few for each curve, not the actual equation.

The Stein-Watkins tables

   http://modular.math.washington.edu/Tables/ecdb/

contains a substantial chunk'' of the curves of conductor . Challenge 4.2.1 amounts to finding the number (and some info about) the curves that are missing from Stein-Watkins in the range of conductors     Next: Weight Up: Computing with Classical Modular Previous: Compute Every Elliptic Curve   Contents
William Stein 2006-10-20